It is often desirable to place antennas near and parallel to metallic surfaces, such as on an aircraft wing. However these surfaces reflect electromagnetic waves out of phase with the incident wave, thus short circuiting the antennas. While naturally occurring materials reflect electromagnetic waves out of phase, artificial magnetic conductors (AMCs) are metasurfaces that reflect incident electromagnetic waves in phase. AMCs are typically composed of unit cells that are less than a half-wavelength and achieve their properties by resonance. Active circuits, for example negative inductors or non-Foster circuits (NFCs), have been employed to increase the bandwidth, thus constituting an active AMC (AAMC). However, the use of negative inductors or non-Foster circuits (NFCs), results in a conditionally stable AAMC that must be carefully designed to avoid oscillation.
AAMCs may improve antennas in a number of ways including 1) increasing antenna bandwidth, as described in references [6] and [11] below, 2) reducing finite ground plane edge effects for antennas mounted on structures to improve their radiation pattern, 3) reducing coupling between antenna elements spaced less than one wavelength apart on structures to mitigate co-site interference, 4) enabling radiation of energy polarized parallel to and directed along structural metal surfaces, and 5) increase the bandwidth and efficiency of cavity-backed slot antennas while reducing cavity size. Use of AAMC technology is particularly applicable for frequencies less than 1 GHz where the physical size of a traditional AMC becomes prohibitive for most practical applications.
An Artificial Magnetic Conductor (AMC) is a type of metamaterial that emulates a magnetic conductor over a limited bandwidth, as described in references [1] and [2] below. An AMC ground plane enables conformal antennas with currents flowing parallel to the surface because parallel image currents in the AMC ground plane enhance their sources. In the prior art, AMCs have been realized with laminated structures composed of a periodic grid of metallic patches distributed on a grounded dielectric layer, as described in references [1] and [3] below.
AMCs may have limited bandwidth. Their bandwidth is proportional to the substrate thickness and permeability, as described in references [1] to [4] below. At VHF-UHF frequencies, the thickness and/or permeability necessary for a reasonable AMC bandwidth is excessively large for antenna ground-plane applications.
The bandwidth limitation of an AMC may be overcome by using an active AMC (AAMC). An AAMC is loaded with non-Foster circuit (NFC) negative inductors, as described in references [1] to [6] below, and an AAMC may have an increased bandwidth of 10× or more compared to an AMC, as described in references [1], [4] and [5] below. When the AMC is loaded with an NFC, its negative inductance in parallel with the substrate inductance results in a much larger net inductance and hence, a much larger AMC bandwidth.
A prior-art AAMC unit cell architecture is shown in FIG. 1. The AAMC has a ground plane 112, a 2.54 cm thick foam substrate 114, a 0.76 mm thick dielectric substrate 116, copper patches 118, which are about 65 mm wide and long, a 10 mm gap 120 between patches 118, a non-Foster circuits (NFC) 122 between patches 118, a wiring access hole 124, and a via to ground 126. The patches 118 are about 50 mm thick.
An Artificial Magnetic Conductor (AMC) is characterized by its resonant frequency, ω0, which is where an incident wave is reflected with 0° phase shift, and by its ±90° bandwidth, which is defined as the frequency range where the reflected phase is within the range |φr|<90°. An AMC response can be accurately modeled over a limited frequency range using an equivalent parallel LRC circuit with LAMC, CAMC, and RAMC as the circuits' inductance, capacitance and resistance respectively, as described in references [1] to [3] and [7] below. The circuit impedance is
                              Z          AMC                =                                            jω              ⁢                                                          ⁢                              L                AMC                                                    1              -                                                ω                  2                                ⁢                                  L                  AMC                                ⁢                                  C                  AMC                                            +                              jω                ⁢                                                                  ⁢                                                      L                    AMC                                    /                                      R                    AMC                                                                                .                                    (        1        )            
The resonant frequency and approximate fractional bandwidth [2] in the limit ω0LAMC<<Z0 are
                                          ω            0                    =                      1                                                            L                  AMC                                ⁢                                  C                  AMC                                                                    ,                                  ⁢                  BW          =                                    ω              0                        ⁢                                          L                AMC                            /                              Z                0                                                    ,                            (        2        )            
where Z0 is the incident wave impedance.
An AMC of the form shown in FIG. 1, where a grounded dielectric substrate is covered with a grid of metallic patches loaded with lumped elements between the patches can be approximated by a simple transmission line model, as described in references [1] and [3] below, which expresses the AMC admittance as the sum of the grid admittance Yg, the load admittance Yload, and the substrate admittance Ysub YAMC=Yg+Yload+Ysub.  (3)Ysub=−j cot(√{square root over (∈μ)} ωd)√{square root over (∈/μ)},  (4)
where d is the dielectric thickness, and ∈ and μ are the substrate's permittivity and permeability respectively. Ysub is expressed in terms of a frequency-dependent inductance, Lsub=−j/(ωYsub) which is approximately a constant Lsub≅μd for thin substrates with √{square root over (∈μ)} ωd<<1. The grid impedance of the metallic squares is capacitive, Yg=jω Cg, and can be accurately estimated analytically, as described in references [2] and [7] below.
The loaded AMC reflection properties can be estimated by equating the LRC circuit parameters of equation (1) to quantities in the transmission line model of equations (3) and (4). If the load is capacitive, then the equivalent LRC circuit parameters areLAMC=Lsub, CAMC=Cg+Cload and RAMC=Rload.  (5)
If the load is inductive as it is in the AAMC of FIG. 1, then they are
                                          L            AMC                    =                                                    L                Load                            ⁢                              L                sub                                                                    L                Load                            +                              L                sub                                                    ,                                  ⁢                              C            AMC                    =                                                    C                g                            ⁢                                                          ⁢              and              ⁢                                                          ⁢                              R                AMC                                      =                                          R                load                            .                                                          (        6        )            
An active AMC is created when the load inductance is negative, and LAMC increases according to equation (6). When Lload<0 and |Lload|>Lsub>0, then LAMC>Lsub, resulting in an increase in the AMC bandwidth, and a decrease in the resonant frequency according to equation (2). When Lload approaches −Lsub, then LAMC is maximized, the resonant frequency is minimized and the bandwidth is maximized. The bandwidth and resonant frequency are prevented from going to infinity and 0 respectively by loss and capacitance in the NFC and the AMC structure.
The AAMC is loaded with non-Foster circuit (NFC) negative inductors, as described in references [1] and [6] below. The NFC is the critical element that enables realization of the AAMC and its high bandwidth. The NFC name alludes to the fact that it circumvents Foster's reactance theorem, as described in reference [8] below, with an active circuit. Details of an NFC circuit design and fabrication are given by White in reference [6] below.
FIG. 2A shows an NFC circuit 130 on a carrier board, which also has capacitors 132, RF (radio frequency) pads 134, and DC (direct current) pads 136. The NFC can be represented by the equivalent circuit model shown in FIG. 2B. In this model, LNFC is the desired negative inductance, RNFC is negative resistance. CNFC and GNFC are positive capacitance and conductance, respectively. In an ideal NFC, RNFC, CNFC and GNFC are all equal to zero. The equivalent circuit parameters vary according to the bias voltage applied and some prior-art NFC circuit parameters are plotted in FIG. 3.
NFCs become unstable when the bias voltage goes too high, when they are subjected to excessive RF power, or when they have detrimental coupling with neighboring NFCs. The instability is manifested as circuit oscillation and emission of radiation from the circuit. When the NFCs in an AAMC become unstable, the AAMC no longer operates as an AMC. One consequence of this in the prior art, as described in reference [1] below, is that it has not been possible to create a dual-polarization AAMC because of instability caused by coupling between neighboring NFCs.
Single-polarization AAMCs have been demonstrated in the prior art, as described in references [1] and [9] below. Coupling between neighboring NFCs in the E plane, meaning between NFCs in neighboring rows, as shown in FIGS. 4A and 4B, causes the single-polarization AAMC to be unstable. As shown in FIG. 4A, patch elements 140 with impedance loads 142 are each on a substrate 146 with a ground plane 148. In order to make the AAMC stable, RF isolation plates 144 must be installed between rows of patch elements 140 in the H plane. The isolation plates 144 span through the substrate 146 from the ground plane 148 to the patch elements 140. The AAMC operates for RF incident polarized perpendicular to the isolation plates 144. Incident radiation polarized along the other axis will be reflected as from a metal conductor because of its interaction with the isolation plates. NFCs next to each other in the H plane do not couple in an unstable manner.
Coaxial versions of the single-polarization AAMC, as shown in FIG. 5A, have been constructed and measured. The coaxial version is convenient for measurement because it can be measured in a bench top setting using a coax transverse-electromagnetic (TEM) cell, as shown in FIG. 5B, that provides direct real-time measurements of AMC phase and amplitude vs. frequency, as described in reference [9] below. In the coax TEM cell, the coax AAMC appears to the incident wave in the coax as an infinite array of unit cells because of its azimuthal periodicity and the PEC boundaries on the radial walls. The fields are polarized radially, and neighboring NFCs do not couple unstably because their separation is perpendicular to the field polarization.
FIG. 5C shows measurements of the coax AAMC that confirm its operation as a stable wideband AMC. The NFC inductance is tuned from −70 to −49.5 nH. The phase and magnitude of a reflected wave vs. frequency is shown. In this AAMC, the resonant frequency can be tuned from approximately 470 MHz to 220 MHz while maintaining stability. When tuned to 263 MHz, as represented by the bold line in FIG. 5C, the ±90° bandwidth is more than 80%, spanning the range from 160 to 391 MHz. The prior-art AAMC has much higher bandwidth than an equivalent passive AMC, as shown in FIG. 6. The AAMC has better than five times the bandwidth of a varactor-loaded AMC at high loading levels.